My Math Forum Finding square root of matrix without eigenvector

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 March 9th, 2019, 06:13 AM #1 Newbie   Joined: Apr 2016 From: Wonderland Posts: 23 Thanks: 0 Finding square root of matrix without eigenvector A is a 2x2 matrix. (0 -2) (2 0) Find the square root of this matrix. I managed to find one of the square root, because I know A is a 90-degree anti-clockwise rotation stretched by a factor of 2. So I just have to "half" that operation and I get (1 -1) (1 1) However, there is another matrix which is the square root of A and I'm struggling to find it. How can I find it without using eigenvectors/eigenvalues?
 March 9th, 2019, 08:44 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,531 Thanks: 1390 what if we do two rotations the other direction? $A = 2 Rot\left(\dfrac \pi 2\right)$ $\sqrt{A} = \sqrt{2} Rot\left(\dfrac{-3\pi}{4}\right)$ $\sqrt{A} = \sqrt{2}\begin{pmatrix}-1 &1\\-1 &-1\end{pmatrix}$ Thanks from topsquark and Appletree
 March 11th, 2019, 04:05 AM #3 Newbie   Joined: Apr 2016 From: Wonderland Posts: 23 Thanks: 0 Thank you romsek. I managed to solve it with your advice and got (-1 1) (-1 -1)

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